How to add noise to background image?
First create a texture in the properties window:



To add the texture in the compositor use an input>texture node, and select the texture you've just created:



Then overlay that on to the background image. You can control the size and shaprpness of the noise by adding a value node and a blur node.


(click on the image to enlarge)

To make it change from frame to frame you can keyframe the values.

Another note: try other forms of noise like Clouds, Musgrave or Stucci to find the texture pattern that matches that of your rendered model's